Hi,
Is there a proof that complex replacement is a valid way to solve a differential equation? I'm lacking some intuition on the idea that under any algebraic manipulations the real and imaginary parts of an expression don't influence each other.
For example, if I'm given:
$$p(D) x = cos(t)$$...
The equations I'm getting when I solve the differential equations seem to imply that the amplitude of oscillation does not vary in time.
For example, if I have
x'' + ω02x = cos(ωt)
If we suppose that ω≠ω0,
then the general solution should look something like:
x(t) = c1cos(ω0t) + c2sin(ω0t)...
The equations I'm getting when I solve the differential equations seem to imply that the amplitude of oscillation does not vary in time.
For example, if I have
x'' + ω02x = cos(ωt)
If we suppose that ω≠ω0,
then the general solution should look something like:
x(t) = c1cos(ω0t) + c2sin(ω0t)...
Hi I'm just having trouble wrapping my head around differential equations with matrices and vectors...
For example:
let y be a vector.
let A(t) be an nxn matrix.
I have the differential equation:
dy/dt = A(t)y
So I think I understand why the solution is
y = ceA(t)
But I'm having trouble...
Hi all,
I'm just beginning calculus and I'm having trouble figuring this one out.
I need to solve this one without using l'hospital's rule.
1. Homework Statement
Find
Limit (sin(4x)/sin(6x)) as x->0
2. Homework Equations
We know that limit (sin(x)/x) as x -> 0 equals...
Hi everyone,
I'm building a white light interferometer and need help choosing and finding a white light source.
I'm using this mirau objective:
http://www.edmundoptics.com/microscopy/infinity-corrected-objectives/nikon-interferometry-objectives/59312
Here is the setup:
I know...
Hi,
I'm just wondering if someone could help me better understand how the Fizeau interferometer works...
http://upload.wikimedia.org/wikipedia/commons/2/2f/Fizeau_interferometer_testing_optical_flat.svg
From my understanding, the source shines light through a collimating lens and the light...
Polar Coordinates --- Graphing the points of when theta<0
Hi everyone,
I'm working with an online graphing program desmos.com. It's great, and actually tons of fun.
I'm currently working with polar coordinates but the only flaw of this grapher is that when working with polar coordinates...
Laser Interferometer--Need advice/opinions about design.
Hey Everyone,
I'm in the midst of designing a laser interferometry system to measure flatness and to level a stainless steel plate. It's a really simple design and I'm wondering what the drawbacks are for this type of system. I'm just...
Radial Flow Water Pump--How to calculate Watts required to power it
Hi all,
I'm currently working on an independent project where I'm building a radial flow water pump to be sent to a village in Senegal. I'm having trouble figuring out what motor to use to power this water pump and how much...